When updating the probability of life across the universe, there are two main observations we have to build on:

Anthropic update: we exist on Earth.
Fermi observation: (we exist on Earth and) we don't see any aliens.

I'll analyse how these two observations affect various theories about life in the universe. In general, we'll see that the anthropic update has a pretty weak effect, while the Fermi observation has a strong effect: those theories that benefit most are those that avoid the downgrade from the Fermi, such as the Zoo hypothesis, or the "human life unusually early" hypothesis.

Grabby and visible aliens

I've argued that an anthropic update on our own existence is actually just a simple Bayesian update; here I'll explain what that means for our updates.

This paper talks about grabby aliens, who would expand across the universe, and stop humans from evolving (if they reached Earth before now). As I've argued, "we exist" and "we have not observed X" are statements that can be treated in exactly the same way. We can combine them to say "there are no visible aliens anywhere near", without distinguishing grabby aliens (who would have stopped our existence) from visible-but-not grabby aliens (who would have changed our observations).

Thus the Fermi observation is saying there are no grabby or visible aliens nearby^[1]. Recall that it's so comparatively easy to cross between stars and galaxies, so advanced aliens would only fail to be grabby if they coordinated to not want to do so.

Rare Earth hypotheses

Some theories posit that life requires a collection of conditions that are very rarely found together.

But rare Earth theories don't differ much, upon updates, from "life is hard" hypotheses.

For example, suppose $T_{0}$ say that life can exist on any planet with rate $ρ$ , while the rare Earth hypothesis, $T_{1}$ , says that life can exist on Earth-like planets with rate $p$ , while Earth-like planets themselves exist with rate $r$ .

But neither the Fermi observation nor the anthropic update will distinguish between these theories. The Fermi observation posits that there are no visible aliens close to Earth; the anthropic updates increases the probability of life similar to us. We can see $T_{1}$ as $T_{0}$ with a different prior on $ρ = p r$ (induced from the priors on $p$ and $r$ ), but both these updates affect $ρ$ .

Now, $T_{0}$ and $T_{1}$ can be distinguished by observation (seeing dead planets with Earth...

Extraterrestrial Life